Batteries are complicated. Besides that, they suck as a storage of power off the grid.
Perhaps it is better to avoid using them, but unfortunately this isn't going to be an option. Reason being that propane generators also suck. These will use up way too much propane, and therefore, will be much too expensive to operate.
Another option is to hook up the car to a deep cycle battery, and let the car charge up the batteries. Car alternators may be able to crank out a lot of juice. It is surprising.
One thing that seems to keep popping up, though. Batteries seem to like to be charged for five hours, or so. Go faster than that, and you may cook it. Slower than that, and your pockets had better very deep, for it will take forever to charge the darn thing.
So, five hours seems to work. Now, a 200 amp-hr battery at the 20-hr rate will only support a 10 amp load in order to get that 200 amps of work out of it. That many amps at 12 volts is only 120 watts. An a/c will pull a lot more than that. You could run a swamp cooler for that long as long as it didn't pull that more than that much current. Swamp coolers do not inspire confidence, though.
A 200 amp-hr battery isn't cheap, either. One of those could run 400 bucks and some change.
You could run a propane generator for a few hours a day. Maybe that five hr number could charge the batteries, and also, maybe you can run an a/c off of it. Five hours for each simultaneously could suffice.
Yeah, it looks like a more complicated problem than the water problem. Climate control takes a lot of juice. That's why I want to think SMALL, because small takes less BTU to heat or to cool.
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